Quantum weirdness on the end of your pencil

INSIDE every pencil, there is a neutron star waiting to get out. To release it, just draw a line. The soft, silvery-grey form of pure carbon found in pencils consists of stacked-up sheets of interlinked carbon atoms. Separate these sheets to obtain gossamer films of carbon just one atom thick and you have a material called graphene, whose properties mimic those of the exotic substances found in collapsed stars.

Graphene even shares properties with materials that were around in the first instants of the big bang. It’s not just about cosmology. According to some enthusiasts, graphene’s ability to conduct electricity promises new and powerful electronic devices fashioned from sheets of carbon cut up into circuitry. And the peculiar way that graphene conducts electricity opens up avenues into some of the weirder areas of quantum physics. It is no wonder that this innocuous material has become one of the hottest substances in physics.

In a sense, though, graphene has been with us forever. “There are at least 10 different sorts of graphite-like carbon, and graphene is the basic building block of them all,” says Andre Geim of the University of Manchester in the UK. The carbon forms include the prosaic – pencil lead and soot – as well as the more peculiar carbon-60 buckyballs and long, hollow carbon nanotubes.

Isolated sheets of graphene, however, have only been studied for the past couple of years – since Geim and his colleagues worked out how to prise the individual layers of carbon apart. Layers of carbon atoms tend to attract each other, which makes it hard to separate them from the stacked sheets of graphite. Yet Geim’s team has found a way that now sounds embarrassingly simple. They etched out some islands in a flake of graphite, stuck some Scotch tape over them and pulled. This stripped off several layers of graphene at a time. By repeating this process, they gradually pared the islands down to just a few layers, or sometimes just a single layer, of graphene.

The first thing Geim and his colleagues did was to wire their graphene sheets up to electrodes to measure their electrical behaviour. As they suspected, they found that graphene conducts electricity&colon; they went on to show that it can be used to make transistors (see “Pencil electronics”).

Things started to get really interesting, though, when Geim’s team looked more closely at graphene’s electrical properties. Inside most materials that conduct electricity, the electrons move erratically, rather like balls in a pinball machine bouncing hither and thither. This electron scattering typically happens when the electrons encounter impurities in the conductor’s crystal lattice that block their way. However, Geim’s team found that graphene was different.

In graphene, the electrons can travel immense distances without scattering, opening up the possibility of ultrafast electronics. No one knows exactly why this happens, though Geim suspects that it is something to do with the near-perfect atomic structure (see Graphic).

The serene way in which graphene’s electrons sail through its crystal lattice is only a hint of the oddness to come, however – their collective behaviour is much more bizarre. Because electrons are quantum objects, they can spread across a wide region of space. And they are electrically charged. This means that electrons interact with one another; the motion of these interacting quantum entities can be viewed collectively as a kind of particle called a quasiparticle, which behaves much the same as a single electron with much larger or smaller mass.

“Graphene can be used to explore phenomena that would be almost impossible to study any other way”

Late last year, Geim’s team discovered that the quasiparticles in graphene are like nothing ever seen in a conducting material. Amazingly, the quasiparticles behave as if they were electrons travelling close to the speed of light. Such fast-moving electrons are usually found only in extreme conditions where particles are accelerated to enormous speeds – for example, close to neutron stars or in the big bang. Making such exotic particles generally taxes the resources of particle physicists, who have to whizz them up in particle accelerators. This means that graphene can be used to explore physical phenomena that would be almost impossible to study experimentally any other way. Geim thinks that graphene will allow us to study some very peculiar phenomena indeed.

“The particle spawns its own antiparticle and then interacts with it, causing it to jitter”

One such phenomenon is the paradox of Zitterbewegung, a German word meaning “jittery motion”. The theory that describes the motion of fast-moving electrons, a combination of relativity and quantum mechanics first developed in 1928 by British physicist Paul Dirac, predicts that such a particle moving from one point to another will not travel in a straight line but will jitter from side to side. According to the theory, that’s because the particle is laden with so much energy that it spawns its own antiparticle – a positively charged positron in the case of an electron. This then interacts with the original particle and causes its trajectory to oscillate. No one has observed Zitterbewegung. That is no surprise, because the jitters are predicted to be too rapid to detect. However, Geim says that a similar effect should operate in graphene, allowing us to test this crucial aspect of quantum mechanics for the first time. Instead of producing positrons, the fast-moving quasiparticles should generate holes, the positively charged carriers of current in many semiconductors. Holes are literally that – gaps in a sea of mobile electrons, moving about just as though they were real particles. Because of these holes, the fast-moving particles in graphene should jitter on the scale of about 100 nanometres or so. Geim believes it might be possible to spot the jitter using a high-resolution microscope that images the density of electrons in materials.

Quantum jitters

Zitterbewegung is not the only spooky quantum phenomenon predicted to happen close to the speed of light. In 1929 the Swedish physicist Oskar Klein predicted that particles near that cosmic speed limit could perform tricks that slower particles cannot. His prediction is a bizarre twist on the phenomenon of quantum tunnelling.

Imagine kicking a football against a solid wall. Everyday experience tells you that the ball will bounce off. Yet in the quantum world, there is a small chance that it will also appear on the other side of the wall. The probability of this falls as the wall becomes wider or higher, and would drop to zero if the wall were infinitely high. In this case, the football would bounce or reflect straight back. At least, that is what would happen to a particle travelling well below the speed of light.

Accelerate a particle to much higher speeds and Klein’s paradox says that the particle can ignore the wall altogether, no matter how high it is. The reason is related to Zitterbewegung&colon; the particle has so much energy that it creates its antiparticle inside the wall. The antiparticle travels through the wall and at the other side creates a replica of the original. It is as if the wall were not even there.

Geim and his colleagues have calculated that it should be possible to see the Klein effect in graphene by applying an electric field across a strip of the material to create a barrier and watching the quasiparticles pass through. “It’s relatively easy to mimic the conditions of Klein’s thought experiment,” he says. “The particles should pass through the barrier without reflection.” Proving the Klein paradox may take some time, however&colon; Geim estimates that it could be as long as two years before the experiment is even set up.

In the meantime, researchers are frantically looking for new and reliable ways to make graphene for practical applications. Geim’s stick-and-peel approach is simple but is not guaranteed to produce just a single graphene layer. Usually it doesn’t. His group has developed an even simpler procedure&colon; merely rubbing a piece of graphite against almost any solid surface will produce a few single-layer flakes. So you really can draw graphene with a pencil.

Though making it remains a challenge, graphene is already proving itself a physicist’s playground. While practical applications of graphene are still a long shot, Geim says, the payoff for physics is guaranteed.

Pencil electronics

Looking to make ultra-small electronic circuits? Then forget fiddling with Lilliputian components made from single molecules or struggling to wire carbon nanotubes together. In 1995 Thomas Ebbesen, then at the NEC Corporation in Tsukuba, Japan, suggested that graphene could be ideal for the job. “If you had a large graphene sheet you could just cut it up,” says Ebbesen.

He envisaged making electronic devices by doping different chemicals into the graphene film. That way, the circuitry would be in one continuous film just one atom thick. “It’s the simplicity that’s the attraction,” says Ebbesen.

Finding ways to shrink electronic components to the molecular scale is vital if we want the trend for faster and cheaper gadgets to continue. It is not possible to carry on shrinking components made from silicon forever&colon; quantum mechanics says that electrons will be able to leak through a nanoscale silicon transistor, causing it to short-circuit. “The industry needs a replacement for silicon by 2020,” says graphene pioneer Andre Geim at the University of Manchester in the UK.

Geim believes he is a step closer to fulfilling Ebbesen’s vision. “We can produce sheets that are 50 micrometres square, which is big enough to cut up into integrated circuits,” he says. The approach would avoid another problem with nanotube electronics too&colon; they cannot be manufactured reliably. “You can make 1000 of them and they will all be different,” says Geim. “Graphene will always be the same.”

Single sheets

Still he doubts that his method of making graphene by tearing sheets of it off graphite will ever be used industrially. “I can’t imagine Intel using our method,” he says.

The race is now on to produce single layers of graphene reliably. In April, a group at the Georgia Institute of Technology in Atlanta led by veteran carbon researcher Walt de Heer reported that single-layer graphene can be grown at the surface of the ceramic material silicon carbide by heating it in a vacuum. This method was first developed in 2002 by a team of researchers from France, Russia and Italy. They showed that the silicon carbide decomposes when it is heated, triggering layer-by-layer growth of graphene films. De Heer and colleagues saw the potential of this approach in the light of graphene’s sudden rise to fame. They have now used it to make graphene ribbons that can be patterned into electronic devices.

Geim says that this may not be the best way to produce graphene electronics in the long run, because it is hard to ensure that the carbon films stop growing after one layer. At Northwestern University in Evanston, Illinois, Rodney Ruoff thinks that clever chemistry might supply the best answer. He has been devising chemical methods for producing single sheets of graphene, and is working on chemically turning graphite oxide into graphene, but “it is still work in progress”, he admits.